Category Archives: Mathematics

Chidambaram on Galois representations (not) associated to abelian varieties over Q

Posted on October 13, 2020 by Persiflage

Today’s post is about a new paper by my student Shiva. Suppose that \(A/\mathbf{Q}\) is a principally polarized abelian variety of dimension \(g\) and \(p\) is a prime. The Galois representation on the \(p\)-torsion points \(A[p]\) gives rise to a … Continue reading →

Posted in Mathematics, Students, Work of my students | Tagged , , , , , , , , | 5 Comments

Families of Hilbert Modular Forms of Partial Weight One.

Posted on June 3, 2020 by Persiflage

Today I would like to talk about a beautiful new theorem of my student Eric Stubley (see also here). The first version of Eric’s result assumed (unknown) cases of the general Ramanujan conjecture for Hilbert modular forms, and relied on … Continue reading →

Posted in Mathematics, Students, Work of my students | Tagged , , , , , , , , , , , | 2 Comments

Picard Groups of Moduli Stacks update

Posted on May 27, 2020 by Persiflage

A tiny update on this post. I was chatting with Benson and realized that I may as well ask him directly for a presentation of the mapping class group of a genus two surface. Perhaps unsurprisingly, it can be found … Continue reading →

Posted in Mathematics | Tagged , , , , | 2 Comments

Picard Groups of Moduli Stacks

Posted on April 30, 2020 by Persiflage

Here are some algebraic geometry musings related to the last post, most of which is hopefully correct. Everything below is secretly over \(\mathbf{Z}[1/6]\) but I think one may as well think about what is happening over \(\mathbf{C}\). Warning: I don’t … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , , | 9 Comments

Chidambaram on genus two curves, II

Posted on April 24, 2020 by Persiflage

We now continue a series of posts on the work of my student Shiva Chidambaram. (Click here for part I.) Today I would like to discuss another project with Shiva that was also joint with David Roberts (no, not David … Continue reading →

Posted in Mathematics, Students, Work of my students | Tagged , , , , , , , , , | 2 Comments

En Passant VIII

Posted on April 23, 2020 by Persiflage

I just found out that Lucien Szpiro recently passed away. I met him only once in late 2018 when I gave the joint NY number theory at CUNY. When I arrived at my hotel (the Gregory) around 10pm, I was … Continue reading →

Posted in Mathematics | Tagged , , , , | Leave a comment

En Passant VII

Posted on April 19, 2020 by Persiflage

Idle question which has surely been asked (and answered!). If \(X^{+}_{\mathrm{nsp}}(p)\) is the modular curve corresponding to the normalizer of the non-split Cartan, then one reason it is hard to find all rational points is that the all factors of … Continue reading →

Posted in Mathematics | Tagged , , | 4 Comments

Chidambaram on genus two curves, I

Posted on April 15, 2020 by Persiflage

Before we start, just to alert you to a minor blogpage design change: all the posts (including this one) which talk about my students work can be accessed in one place by clicking the “work of my students” tab just … Continue reading →

Posted in Mathematics, Students | Tagged , , , , , , , , , , , , | 8 Comments

How to reject a paper

Posted on March 31, 2020 by Persiflage

I just had the paper discussed in this post very quickly rejected. Since it was such a short paper, I thought it not too unreasonable to submit it to a strong journal, so I am not terribly disappointed. I can … Continue reading →

Posted in Mathematics | Tagged , | 8 Comments

The Hausdorff Trimester has been indefinitely postponed

Posted on March 18, 2020 by Persiflage

I’m not sure if this is 100% official yet, but the Hausdorff Trimester scheduled for this summer has been (unsurprisingly) postponed. This is probably no great surprise to many of you. We have hopes to reschedule it again (perhaps for … Continue reading →

Posted in Mathematics | Tagged , , , , | 1 Comment